Abstract

Using analysis and numerical simulation, we have investigated near-infrared and mid-infrared second-harmonic generation (SHG) and sum frequency generation (SFG) in crystal silicon (SOI) waveguides that possess a strong second-order nonlinear susceptibility by virtue of a Si3N4 straining layer applied directly to the top surface of the waveguide. This layer induces anisotropic compressive strain in the waveguide core. Using the technique of TE/TM mode birefringence, we have derived waveguide geometries for both slab and strip channel waveguides that offer perfect phase matching of three lightwaves for SHG/SFG along a uniform waveguide, thereby offering the prospect of efficient wavelength conversion in monolithic silicon photonics.

© 2011 OSA

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  1. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
    [CrossRef] [PubMed]
  2. J. Fage-Pedersen, L. H. Frandsen, A. V. Lavrinenko, and P. I. Borel, “A linear electro-optic effect in silicon,” in IEEE 3rd International Conference on Group IV Photonics, 37-39 (2006).
  3. F. Bianco, E. Borga, A. Yeremian, B. Dierre, K. Fedus, P. Bettoni, A. Pitanti, R. Pierbon, M. Ghulinyan, G. Pucker, M. Cazzanelli, and L. Pavesi, “Second-order susceptibility ?(2) in Si waveguides,” paper WB2, IEEE 8th International Conference on Group IV Photonics, London (13 September 2011).
  4. N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically-poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
    [CrossRef]
  5. N. K. Hon, K. K. Tsia, D. R. Solli, B. Jalali, and J. B. Khurgin, "Stress-induced ?(2) in silicon - comparison between theoretical and experimental values,” in IEEE 6th International Conference on Group IV Photonics, San Francisco, CA (9-11 September 2009).
  6. B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express 19(18), 17212–17219 (2011).
    [CrossRef] [PubMed]
  7. I. Avrutsky, R. Soref, and W. Buchwald, “Mid-infrared optical parametric oscillators based on uniform GaP waveguides,” Opt. Express 18(19), 20370–20383 (2010).
    [CrossRef] [PubMed]
  8. T. Baehr-Jones, M. Hochberg, G. Wang, R. Lawson, Y. Liao, P. A. Sullivan, L. Dalton, A. K.-Y. Jen, and A. Scherer, “Optical modulation and detection in slotted Silicon waveguides,” Opt. Express 13(14), 5216–5226 (2005).
    [CrossRef] [PubMed]
  9. J. I. Dadap, N. C. Panoiu, X. Chen, I.-W. Hsieh, X. Liu, C.-Y. Chou, E. Dulkeith, S. J. McNab, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
    [CrossRef] [PubMed]
  10. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989), p. 31.
  11. T. K. Lim and H. J. Melchior, “Effective index method for generalized waveguide dispersion characteristics analysis of optical channel waveguides,” Electron. Lett. 27(11), 917–918 (1991).
    [CrossRef]

2011

2010

2009

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically-poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

2008

2006

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

2005

1991

T. K. Lim and H. J. Melchior, “Effective index method for generalized waveguide dispersion characteristics analysis of optical channel waveguides,” Electron. Lett. 27(11), 917–918 (1991).
[CrossRef]

Andersen, K. N.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Avrutsky, I.

Baehr-Jones, T.

Bjarklev, A.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Bolten, J.

Borel, P. I.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Buchwald, W.

Chen, X.

Chmielak, B.

Chou, C.-Y.

Dadap, J. I.

Dalton, L.

Dulkeith, E.

Fage-Pedersen, J.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Frandsen, L. H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Green, W. M. J.

Hansen, O.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Hochberg, M.

Hon, N. K.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically-poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

Hsieh, I.-W.

Jacobsen, R. S.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Jalali, B.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically-poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

Jen, A. K.-Y.

Kristensen, M.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Kurz, H.

Lavrinenko, A. V.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Lawson, R.

Liao, Y.

Lim, T. K.

T. K. Lim and H. J. Melchior, “Effective index method for generalized waveguide dispersion characteristics analysis of optical channel waveguides,” Electron. Lett. 27(11), 917–918 (1991).
[CrossRef]

Liu, X.

Matheisen, C.

McNab, S. J.

Melchior, H. J.

T. K. Lim and H. J. Melchior, “Effective index method for generalized waveguide dispersion characteristics analysis of optical channel waveguides,” Electron. Lett. 27(11), 917–918 (1991).
[CrossRef]

Merget, F.

Moulin, G.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Nagel, M.

Osgood, R. M.

Ou, H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Panoiu, N. C.

Peucheret, C.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Ripperda, C.

Scherer, A.

Sekaric, L.

Solli, D. R.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically-poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

Soref, R.

Sullivan, P. A.

Tsia, K. K.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically-poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

Vlasov, Y. A.

Wahlbrink, T.

Waldow, M.

Wang, G.

Xia, F.

Zsigri, B.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically-poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

Electron. Lett.

T. K. Lim and H. J. Melchior, “Effective index method for generalized waveguide dispersion characteristics analysis of optical channel waveguides,” Electron. Lett. 27(11), 917–918 (1991).
[CrossRef]

Nature

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[CrossRef] [PubMed]

Opt. Express

Other

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989), p. 31.

J. Fage-Pedersen, L. H. Frandsen, A. V. Lavrinenko, and P. I. Borel, “A linear electro-optic effect in silicon,” in IEEE 3rd International Conference on Group IV Photonics, 37-39 (2006).

F. Bianco, E. Borga, A. Yeremian, B. Dierre, K. Fedus, P. Bettoni, A. Pitanti, R. Pierbon, M. Ghulinyan, G. Pucker, M. Cazzanelli, and L. Pavesi, “Second-order susceptibility ?(2) in Si waveguides,” paper WB2, IEEE 8th International Conference on Group IV Photonics, London (13 September 2011).

N. K. Hon, K. K. Tsia, D. R. Solli, B. Jalali, and J. B. Khurgin, "Stress-induced ?(2) in silicon - comparison between theoretical and experimental values,” in IEEE 6th International Conference on Group IV Photonics, San Francisco, CA (9-11 September 2009).

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Figures (6)

Fig. 1
Fig. 1

The modal indices for TE (red) and TM (blue) fundamental modes at the wavelength of 2.94μm (solid) and 1.47μm (dashed) as a function of the silicon core layer thickness in the Si3N4/Si/SiO2 planar waveguide structure. The inset shows the waveguide structure.

Fig. 2
Fig. 2

Profiles of the modal fields vs Y coordinate for the pump (solid red, λ = 2.94μm, electric field strength of TE0 mode) and second harmonic (dashed blue, λ = 1.47μm, normal component of the TM0 mode E-field). The Si core width extends from Y = 0.0 to Y = 0.212 μm.

Fig. 3
Fig. 3

Limitations for the choice of wavelength λ1 and λ2 for sum- frequency generation: shadowed area shows allowed wavelengths. The relation between the wavelengths for a given value of the parameter a is illustrated by dashed lines.

Fig. 4
Fig. 4

Optimal core thickness d versus SFG signal wavelength λs for several representative values of a = 0.35, 0.37, 0.40, 0.44, 0.50. Polarizations: TE for both pump waves and TM for the signal at sum frequency.

Fig. 5
Fig. 5

Dispersion curves for the TE00 mode at the pump wavelength, λp = 2.94μm (solid, shades of red-pink) and TM00 mode at the second harmonic wavelength, λs = 1.47μm (dashed, shades of blue-cyan), as a function of the Si core thickness d, for the values of the strip width w, from top to bottom, w = ∞, 5μm, 2.5μm, 1.25μm. Bold black dots indicate the phase matching condition for SHG. The inset shows the optimal thickness of the core versus the strip width.

Fig. 6
Fig. 6

Left: The overlap integral squared as a function of the strip width. The core thickness is optimized as shown in the inset in Fig. 5. Right: The modal fields in the ridge waveguide calculated using the effective index approach: TE00 mode at the pump wavelength λp = 2.94μm (top) and TM00 mode at the second-harmonic signal wavelength (bottom). The field of view in both cases is 4.5μm × 2.0 μm. False colors from red to purple indicate relative strength of the electric field from maximal to minimal value.

Equations (12)

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n Si ( λ )= 1+ 10.6684293 λ 2 λ 2 0.301516485 2 + 0.003043475 λ 2 λ 2 1.13475115 2 + 1.54133408 λ 2 λ 2 1104.0 2 ,
n SiO2 ( λ )= 1+ 0.6961663 λ 2 λ 2 0.0684043 2 + 0.4079426 λ 2 λ 2 0.1162414 2 + 0.8974794 λ 2 λ 2 9.896161 2 ,
n Si3N4 ( λ )= 4+ 2.7 λ 2 λ 2 12.0 2 .
1 λ 1 + 1 λ 2 = 1 λ s ,
an( λ s /a )+( 1a )n( λ s /( 1a ) )=n( λ s ),
a= λ s λ 1 =1 λ s λ 2 ,
λ a λ b = a min <a< a max = λ b λ a λ b ,
λ a < λ s <( 1a ) λ b , if a 1 2 ,
λ a < λ s <a λ b , if a< 1 2
η SHG = 2 π 2 ε 0 c λ p 2 n s * n p * 2 I 2 χ (2) 2
I= core E sy ( x,y ) E px 2 ( x,y )dxdy
E 2 ( x,y )dxdy =1,

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